Summary: Journal of the Mechanics and Physics of Solids
53 (2005) 227­248
www.elsevier.com/locate/jmps
Brittle fracture dynamics with arbitrary paths
III. The branching instability under general
loading
M. Adda-Bedia
Laboratoire de Physique Statistique de l'Ecole Normale SupÃerieure, 24 rue Lhomond,
F­75231 Paris Cedex 05, France
Received 14 November 2003; received in revised form 14 May 2004
Abstract
The dynamic propagation of a bifurcated crack under arbitrary loading is studied. Under plane
loading conÿgurations, it is shown that the model problem of the determination of the dynamic
stress intensity factors after branching is similar to the anti-plane crack branching problem.
By analogy with the exact results of the mode III case, the energy release rate immediately
after branching under plane situations is expected to be maximized when the branches start to
propagate quasi-statically. Therefore, the branching of a single propagating crack under mode I
loading should be energetically possible when its speed exceeds a threshold value. The critical
velocity for branching of the initial single crack depends only weakly on the criterion applied
for selecting the paths followed by the branches. However, the principle of local symmetry